We experimentally demonstrated significant enhancement of terahertz-wave absorption in monolayer graphene by simply sandwiching monolayer graphene between two dielectric media in a total internal reflection geometry. In going through this structure, the evanescent wave of the incident terahertz beam interacts with the sandwiched graphene layer multiple (up to four) times at varying incidence angles. We observed extremely large attenuation (up to ∼70% per reflection), especially for s-polarized radiation. The experimental results are quantitatively consistent with our calculations, where we modeled the experiment as an electromagnetic wave reflection process in monolayer graphene. We also derived analytical expressions for the absorptance, showing that the absorptance is proportional to the amount of Joule heating on the graphene surface induced by the terahertz radiation.